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We show that the multicomponent Kardar-Parisi-Zhang equation describes the low-energy theory for phase fluctuations in a $\mathbb{Z}_{2}$ degenerate non-equilibrium driven-dissipative condensate with global $U(1)\times U(1)$ symmetry. Using dynamical renormalisation group in spatial dimension $d=1$, we demonstrate that coupled stochastic complex Ginsburg-Landau equations exhibit an emergent stationary distribution, enforcing KPZ dynamical exponent $z=3/2$ and static roughness exponent $\chi=1/2$ for both components. By tuning intercomponent interactions, the system can access other regimes, including a fragmented condensate regime from a dynamical instability in the phase fluctuations, as well as a spacetime vortex regime driven by the non-linear terms in the coupled KPZ equations. In stable regimes, we show that in specific submanifolds relevant to polaritons, the RG fixed point offers a transformation to decoupled KPZ equations. Our findings have broad implications for understanding multicomponent KPZ systems in the long-wavelength limit., Comment: 7 pages, 3 figures with supplemental materials attached

Genetic screens mediated via CRISPR-Cas9 combined with high-content readouts have emerged as powerful tools for biological discovery. However, computational analyses of these screens come with additional challenges beyond those found with standard scRNA-seq analyses. For example, perturbation-induced variations of interest may be subtle and masked by other dominant source of variation shared with controls, and variable guide efficiency results in some cells not undergoing genetic perturbation despite expressing a guide RNA. While a number of methods have been developed to address the former problem by explicitly disentangling perturbation-induced variations from those shared with controls, less attention has been paid to the latter problem of noisy perturbation labels. To address this issue, here we propose ContrastiveVI+, a generative modeling framework that both disentangles perturbation-induced from non-perturbation-related variations while also inferring whether cells truly underwent genomic edits. Applied to three large-scale Perturb-seq datasets, we find that ContrastiveVI+ better recovers known perturbation-induced variations compared to previous methods while successfully identifying cells that escaped the functional consequences of guide RNA expression. An open-source implementation of our model is available at \url{https://github.com/insitro/contrastive_vi_plus}., Comment: 15 pages, 4 figures, will be included in the AIDrugX workshop in Neurips 2024

Coboundary expansion is a high dimensional generalization of the Cheeger constant to simplicial complexes. Originally, this notion was motivated by the fact that it implies topological expansion, but nowadays a significant part of the motivation stems from its deep connection to problems in theoretical computer science such as agreement expansion in the low soundness regime. In this paper, we prove coboundary expansion with non-Abelian coefficients for the coset complex construction of Kaufman and Oppenheim. Our proof uses a novel global argument, as opposed to the local-to-global arguments that are used to prove cosystolic expansion.

Observations of Faraday rotation and synchrotron emission in galaxy clusters imply large-scale magnetic fields with $\mu\mathrm{G}$ strengths possibly extending back to $z=4$. Non-radiative cosmological simulations of galaxy clusters show a comparably slow magnetic field growth that only saturates at late times. We include galaxy formation physics and find a significantly accelerated magnetic field growth. We identify three crucial stages in the magnetic field evolution. 1) At high redshift, the central dominant galaxy serves as the prime agent that magnetizes not only its immediate vicinity but also most of the forming protocluster through a combination of a small-scale dynamo induced by gravitationally driven, compressive turbulence and stellar and active galactic nuclei feedback that distribute the magnetic field via outflows. 2) This process continues as other galaxies merge into the forming cluster in subsequent epochs, thereby transporting their previously amplified magnetic field to the intracluster medium (ICM) through ram pressure stripping and galactic winds. 3) At lower redshift, gas accretion and frequent cluster mergers trigger additional small-scale dynamo processes, thereby preventing the decay of the magnetic field and fostering the increase of the magnetic coherence scale. We show that the magnetic field observed today in the weakly collisional ICM is consistently amplified on collisional scales. Initially, this occurs in the collisional interstellar medium during protocluster assembly, and later in the ICM on the magnetic coherence scale, which always exceeds the particle mean free path, supporting the use of magneto-hydrodynamics for studying the cluster dynamo. We generate synthetic Faraday rotation measure observations of protoclusters, highlighting the potential for studying magnetic field growth during the onset of cluster formation at cosmic dawn., Comment: 23 pages, 15 figures, submitted to A&A

Future wireless systems are expected to deliver significantly higher quality-of-service (QoS) albeit with fewer energy resources for diverse, already existing and also novel wireless applications. The optimal resource allocation for a system in this regard could be investigated by reducing the overall power available at the expense of reduced QoS for the inefficient users. In other words, we maximize the system energy efficiency by achieving power saving through a minimal back-off in terms of QoS. In this paper, we investigate the energy efficiency vs. delivered QoS trade-off for the rate-splitting multiple access (RSMA) assisted downlink system. We first determine the user grouping with a normalised channel similarity metric so as to allow a large number of users with non-zero achievable private message rates. Through the private message removal (PMR) of these users, we aim to investigate the QoS vs. energy efficiency trade-off. Numerical results indicate a peak of ~$10\%$ increase in the network energy efficiency for the proposed normalised channel similarity metric based user grouping with scheduled PMR., Comment: 5 pages, 4 figures, IEEE SPAWC 2024 Conference version

Accurate 3D object detection in real-world environments requires a huge amount of annotated data with high quality. Acquiring such data is tedious and expensive, and often needs repeated effort when a new sensor is adopted or when the detector is deployed in a new environment. We investigate a new scenario to construct 3D object detectors: learning from the predictions of a nearby unit that is equipped with an accurate detector. For example, when a self-driving car enters a new area, it may learn from other traffic participants whose detectors have been optimized for that area. This setting is label-efficient, sensor-agnostic, and communication-efficient: nearby units only need to share the predictions with the ego agent (e.g., car). Naively using the received predictions as ground-truths to train the detector for the ego car, however, leads to inferior performance. We systematically study the problem and identify viewpoint mismatches and mislocalization (due to synchronization and GPS errors) as the main causes, which unavoidably result in false positives, false negatives, and inaccurate pseudo labels. We propose a distance-based curriculum, first learning from closer units with similar viewpoints and subsequently improving the quality of other units' predictions via self-training. We further demonstrate that an effective pseudo label refinement module can be trained with a handful of annotated data, largely reducing the data quantity necessary to train an object detector. We validate our approach on the recently released real-world collaborative driving dataset, using reference cars' predictions as pseudo labels for the ego car. Extensive experiments including several scenarios (e.g., different sensors, detectors, and domains) demonstrate the effectiveness of our approach toward label-efficient learning of 3D perception from other units' predictions.

We study which machine learning algorithms have tight generalization bounds. First, we present conditions that preclude the existence of tight generalization bounds. Specifically, we show that algorithms that have certain inductive biases that cause them to be unstable do not admit tight generalization bounds. Next, we show that algorithms that are sufficiently stable do have tight generalization bounds. We conclude with a simple characterization that relates the existence of tight generalization bounds to the conditional variance of the algorithm's loss.

This work introduces Sample-Efficient Speech Diffusion (SESD), an algorithm for effective speech synthesis in modest data regimes through latent diffusion. It is based on a novel diffusion architecture, that we call U-Audio Transformer (U-AT), that efficiently scales to long sequences and operates in the latent space of a pre-trained audio autoencoder. Conditioned on character-aware language model representations, SESD achieves impressive results despite training on less than 1k hours of speech - far less than current state-of-the-art systems. In fact, it synthesizes more intelligible speech than the state-of-the-art auto-regressive model, VALL-E, while using less than 2% the training data., Comment: Interspeech 2024

We study the impact of forbidding short cycles to the edge density of $k$-planar graphs; a $k$-planar graph is one that can be drawn in the plane with at most $k$ crossings per edge. Specifically, we consider three settings, according to which the forbidden substructures are $3$-cycles, $4$-cycles or both of them (i.e., girth $\ge 5$). For all three settings and all $k\in\{1,2,3\}$, we present lower and upper bounds on the maximum number of edges in any $k$-planar graph on $n$ vertices. Our bounds are of the form $c\,n$, for some explicit constant $c$ that depends on $k$ and on the setting. For general $k \geq 4$ our bounds are of the form $c\sqrt{k}n$, for some explicit constant $c$. These results are obtained by leveraging different techniques, such as the discharging method, the recently introduced density formula for non-planar graphs, and new upper bounds for the crossing number of $2$-- and $3$-planar graphs in combination with corresponding lower bounds based on the Crossing Lemma., Comment: Appears in the Proceedings of the 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

Current language models demonstrate remarkable proficiency in text generation. However, for many applications it is desirable to control attributes, such as sentiment, or toxicity, of the generated language -- ideally tailored towards each specific use case and target audience. For auto-regressive language models, existing guidance methods are prone to decoding errors that cascade during generation and degrade performance. In contrast, text diffusion models can easily be guided with, for example, a simple linear sentiment classifier -- however they do suffer from significantly higher perplexity than auto-regressive alternatives. In this paper we use a guided diffusion model to produce a latent proposal that steers an auto-regressive language model to generate text with desired properties. Our model inherits the unmatched fluency of the auto-regressive approach and the plug-and-play flexibility of diffusion. We show that it outperforms previous plug-and-play guidance methods across a wide range of benchmark data sets. Further, controlling a new attribute in our framework is reduced to training a single logistic regression classifier., Comment: ACL Findings 2024

In this work, we introduce Gemma 2, a new addition to the Gemma family of lightweight, state-of-the-art open models, ranging in scale from 2 billion to 27 billion parameters. In this new version, we apply several known technical modifications to the Transformer architecture, such as interleaving local-global attentions (Beltagy et al., 2020a) and group-query attention (Ainslie et al., 2023). We also train the 2B and 9B models with knowledge distillation (Hinton et al., 2015) instead of next token prediction. The resulting models deliver the best performance for their size, and even offer competitive alternatives to models that are 2-3 times bigger. We release all our models to the community.

Grothendieck fibrations are fundamental in capturing the concept of dependency, notably in categorical semantics of type theory and programming languages. A relevant instance are Dialectica fibrations which generalise G\"odel's Dialectica proof interpretation and have been widely studied in recent years. We characterise when a given fibration is a generalised, dependent Dialectica fibration, namely an iterated completion of a fibration by dependent products and sums (along a given class of display maps). From a technical perspective, we complement the work of Hofstra on Dialectica fibrations by an internal viewpoint, categorifying the classical notion of quantifier-freeness. We also generalise both Hofstra's and Trotta et al.'s work on G\"odel fibrations to the dependent case, replacing the class of cartesian projections in the base category by arbitrary display maps. We discuss how this recovers a range of relevant examples in categorical logic and proof theory. Moreover, as another instance, we introduce Hilbert fibrations, providing a categorical understanding of Hilbert's $\epsilon$- and $\tau$-operators well-known from proof theory., Comment: 35 pages. Comments welcome! v3: Small corrections and additions of references

The high contrast and spatial resolution requirements for directly imaging exoplanets requires effective coordination of wavefront control, coronagraphy, observation techniques, and post-processing algorithms. However, even with this suite of tools, identifying and retrieving exoplanet signals embedded in resolved scattered light regions can be extremely challenging due to the increased noise from scattered light off the circumstellar disk and the potential misinterpretation of the true nature of the detected signal. This issue pertains not only to imaging terrestrial planets in habitable zones within zodiacal and exozodiacal emission but also to young planets embedded in circumstellar, transitional, and debris disks. This is particularly true for H{\alpha} detection of exoplanets in transitional disks. This work delves into recent H{\alpha} observations of three transitional disks systems with MagAO-X, an extreme adaptive optics system for the 6.5-meter Magellan Clay telescope. We employed angular differential imaging (ADI) and simultaneous spectral differential imaging (SSDI) in combination with KLIP, a PCA algorithm in post-processing, for optimal starlight suppression and quasi-static noise removal. We discuss the challenges in protoplanet identification with MagAO-X in environments rich with scattered and reflected light from disk structures and explore a potential solution for removing noise contributions from real astronomical objects with current observation and post-processing techniques.

We present the preliminary design of GMagAO-X, the first-light high-contrast imager planned for the Giant Magellan Telescope. GMagAO-X will realize the revolutionary increase in spatial resolution and sensitivity provided by the 25 m GMT. It will enable, for the first time, the spectroscopic characterization of nearby potentially habitable terrestrial exoplanets orbiting late-type stars. Additional science cases include: reflected light characterization of mature giant planets; measurement of young extrasolar giant planet variability; characterization of circumstellar disks at unprecedented spatial resolution; characterization of benchmark stellar atmospheres at high spectral resolution; and mapping of resolved objects such as giant stars and asteroids. These, and many more, science cases will be enabled by a 21,000 actuator extreme adaptive optics system, a coronagraphic wavefront control system, and a suite of imagers and spectrographs. We will review the science-driven performance requirements for GMagAO-X, which include achieving a Strehl ratio of 70% at 800 nm on 8th mag and brighter stars, and post-processed characterization at astrophysical flux-ratios of 1e-7 at 4 lambda/D (26 mas at 800 nm) separation. We will provide an overview of the resulting mechanical, optical, and software designs optimized to deliver this performance. We will also discuss the interfaces to the GMT itself, and the concept of operations. We will present an overview of our end-to-end performance modeling and simulations, including the control of segment phasing, as well as an overview of prototype lab demonstrations. Finally, we will review the results of Preliminary Design Review held in February, 2024., Comment: Presented at SPIE Astronomical Telescopes

MagAO-X is the coronagraphic extreme adaptive optics system for the 6.5 m Magellan Clay Telescope. We report the results of commissioning the first phase of MagAO-X. Components now available for routine observations include: the >2 kHz high-order control loop consisting of a 97 actuator woofer deformable mirror (DM), a 2040 actuator tweeter DM, and a modulated pyramid wavefront sensor (WFS); classical Lyot coronagraphs with integrated low-order (LO) WFS and control using a third 97-actuator non-common path correcting (NCPC) DM; broad band imaging in g, r, i, and z filters with two EMCCDs; simultaneous differential imaging in H-alpha; and integral field spectroscopy with the VIS-X module. Early science results include the discovery of an H-alpha jet, images of accreting protoplanets at H-alpha, images of young extrasolar giant planets in the optical, discovery of new white dwarf companions, resolved images of evolved stars, and high-contrast images of circumstellar disks in scattered light in g-band (500 nm). We have commenced an upgrade program, called "Phase II", to enable high-contrast observations at the smallest inner working angles possible. These upgrades include a new 952 actuator NCPC DM to enable coronagraphic wavefront control; phase induced amplitude apodization coronagraphs; new fast cameras for LOWFS and Lyot-LOWFS; and real-time computer upgrades. We will report the status of these upgrades and results of first on-sky testing in March-May 2024., Comment: Presented at SPIE Astronomical Telescopes

High-contrast imaging data analysis depends on removing residual starlight from the host star to reveal planets and disks. Most observers do this with principal components analysis (i.e. KLIP) using modes computed from the science images themselves. These modes may not be orthogonal to planet and disk signals, leading to over-subtraction. The wavefront sensor data recorded during the observation provide an independent signal with which to predict the instrument point-spread function (PSF). MagAO-X is an extreme adaptive optics (ExAO) system for the 6.5-meter Magellan Clay telescope and a technology pathfinder for ExAO with GMagAO-X on the upcoming Giant Magellan Telescope. MagAO-X is designed to save all sensor information, including kHz-speed wavefront measurements. Our software and compressed data formats were designed to record the millions of training samples required for machine learning with high throughput. The large volume of image and sensor data lets us learn a PSF model incorporating all the information available. This will eventually allow us to probe smaller star-planet separations at greater sensitivities, which will be needed for rocky planet imaging., Comment: 9 pages, 5 figures, proceedings of Adaptive Optics Systems IX at SPIE Astronomical Telescopes + Instrumentation 2024

Simplicial type theory extends homotopy type theory with a directed path type which internalizes the notion of a homomorphism within a type. This concept has significant applications both within mathematics -- where it allows for synthetic (higher) category theory -- and programming languages -- where it leads to a directed version of the structure identity principle. In this work, we construct the first types in simplicial type theory with non-trivial homomorphisms. We extend simplicial type theory with modalities and new reasoning principles to obtain triangulated type theory in order to construct the universe of discrete types $\mathcal{S}$. We prove that homomorphisms in this type correspond to ordinary functions of types i.e., that $\mathcal{S}$ is directed univalent. The construction of $\mathcal{S}$ is foundational for both of the aforementioned applications of simplicial type theory. We are able to define several crucial examples of categories and to recover important results from category theory. Using $\mathcal{S}$, we are also able to define various types whose usage is guaranteed to be functorial. These provide the first complete examples of the proposed directed structure identity principle.

Developing prompt-based methods with Large Language Models (LLMs) requires making numerous decisions, which give rise to a combinatorial search problem. For example, selecting the right pre-trained LLM, prompt, and hyperparameters to attain the best performance for a task typically necessitates evaluating an expoential number of candidates on large validation sets. This exhaustive evaluation can be time-consuming and costly, as both inference and evaluation of LLM-based approaches are resource-intensive. Worse, a lot of computation is wasted: Many hyper-parameter settings are non-competitive, and many samples from the validation set are highly correlated - providing little or no new information. So, if the goal is to identify the best method, it can be done far more efficiently if the validation samples and methods are selected adaptively. In this paper, we propose a novel method to address this challenge. We lean on low-rank matrix factorization to fill in missing evaluations and on multi-armed bandits to sequentially identify the next (method, validation sample)-pair to evaluate. We carefully assess the efficacy of our approach on several competitive benchmark problems and show that it can identify the top-performing method using only 5-15% of the typically needed resources -- resulting in a staggering 85-95% LLM cost savings.

This paper presents a novel approach to aligning large language models (LLMs) with individual human preferences, sometimes referred to as Reinforcement Learning from \textit{Personalized} Human Feedback (RLPHF). Given stated preferences along multiple dimensions, such as helpfulness, conciseness, or humor, the goal is to create an LLM without re-training that best adheres to this specification. Starting from specialized expert LLMs, each trained for one such particular preference dimension, we propose a black-box method that merges their outputs on a per-token level. We train a lightweight Preference Control Model (PCM) that dynamically translates the preference description and current context into next-token prediction weights. By combining the expert models' outputs at the token level, our approach dynamically generates text that optimizes the given preference. Empirical tests show that our method matches or surpasses existing preference merging techniques, providing a scalable, efficient alternative to fine-tuning LLMs for individual personalization.

Motivated by communication systems with constrained complexity, we consider the problem of input symbol selection for discrete memoryless channels (DMCs). Given a DMC, the goal is to find a subset of its input alphabet, so that the optimal input distribution that is only supported on these symbols maximizes the capacity among all other subsets of the same size (or smaller). We observe that the resulting optimization problem is non-concave and non-submodular, and so generic methods for such cases do not have theoretical guarantees. We derive an analytical upper bound on the capacity loss when selecting a subset of input symbols based only on the properties of the transition matrix of the channel. We propose a selection algorithm that is based on input-symbols clustering, and an appropriate choice of representatives for each cluster, which uses the theoretical bound as a surrogate objective function. We provide numerical experiments to support the findings.

AGN bubbles in cool-core galaxy clusters are believed to significantly facilitate the transport of cosmic ray electrons (CRe) throughout the cluster. Recent radio observations are revealing complex morphologies of cluster diffuse emission, potentially linked to interactions between AGN bursts and the cluster environment. We perform three-dimensional magneto-hydrodynamical simulations of binary cluster mergers and inject a bi-directional jet at the center of the main cluster. Kinetic, thermal, magnetic and CRe energy are included in the jet and we use the two-fluid formalism to model the CRe component. We explore a wide range of cluster merger and jet parameters. We discuss the formation of various wide-angle-tail (WAT) and X-shaped sources in the course of the early evolution of the jet and merger. During the last phase of the evolution, we find that the CR material efficiently permeates the central region of the cluster reaching radii of $\sim1$--2 Mpc within $\sim5$--6 Gyr, depending on the merger mass ratio. We find that solenoidal turbulence dominates during the binary merger and explore the possibility for the CRe jet material to be re-accelerated by super-Alfv\`enic turbulence and contribute to cluster scale radio emission. We find that the emission can be volume-filing, $\gtrsim 70$\%. Finally, we study the merger shock interaction with the CRe material and show that it is unlikely that this material significantly contributes to the radio relic emission associated with the shocks. We suggest that multiple jet outbursts and/or off-center radio galaxies would increase the likelihood of detecting these merger shocks in the radio due to shock re-acceleration., Comment: 29 pages, 18 figures, submitted to ApJ, comments welcome

JWST has recently revealed a large population of accreting black holes (BHs) in the early Universe. Even after accounting for possible systematic biases, the high-z $M_*-M_{\rm \rm bh}$ relation derived from these objects by Pacucci et al. (2023 P23 relation) is above the local scaling relation by $>3\sigma$. To understand the implications of potentially overmassive high-z BH populations, we study the BH growth at $z\sim4-7$ using the $[18~\mathrm{Mpc}]^3$ BRAHMA suite of cosmological simulations with systematic variations of heavy seed models that emulate direct collapse black hole (DCBH) formation. In our least restrictive seed model, we place $\sim10^5~M_{\odot}$ seeds in halos with sufficient dense and metal-poor gas. To model conditions for direct collapse, we impose additional criteria based on a minimum Lyman Werner flux (LW flux $=10~J_{21}$), maximum gas spin, and an environmental richness criterion. The high-z BH growth in our simulations is merger dominated, with a relatively small contribution from gas accretion. For the most restrictive simulation that includes all the above seeding criteria for DCBH formation, the high-z $M_*-M_{\rm bh}$ relation falls significantly below the P23 relation (by factor of $\sim10$ at $z\sim4$). Only by excluding the spin and environment based criteria, and by assuming $\lesssim750~\mathrm{Myr}$ delay times between host galaxy mergers and subsequent BH mergers, are we able to reproduce the P23 relation. Overall, our results suggest that if high-z BHs are indeed systematically overmassive, assembling them would require more efficient heavy seeding channels, higher initial seed masses, additional contributions from lighter seeds to BH mergers, and / or more efficient modes for BH accretion., Comment: 21 pages, 15 figures

This second paper presents an in-depth analysis of the composition of the planetary material that has been accreted onto seven white dwarfs with circumstellar dust and gas emission discs with abundances reported in Paper I. The white dwarfs are accreting planetary bodies with a wide range of oxygen, carbon, and sulfur volatile contents, including one white dwarf that shows the most enhanced sulfur abundance seen to date. Three white dwarfs show tentative evidence (2-3$\sigma$) of accreting oxygen-rich material, potentially from water-rich bodies, whilst two others are accreting dry, rocky material. One white dwarf is accreting a mantle-rich fragment of a larger differentiated body, whilst two white dwarfs show an enhancement in their iron abundance and could be accreting core-rich fragments. Whilst most planetary material accreted by white dwarfs display chondritic or bulk Earth-like compositions, these observations demonstrate that core-mantle differentiation, disruptive collisions, and the accretion of core-mantle differentiated material are important. Less than one percent of polluted white dwarfs host both observable circumstellar gas and dust. It is unknown whether these systems are experiencing an early phase in the disruption and accretion of planetary bodies, or alternatively if they are accreting larger planetary bodies. From this work there is no substantial evidence for significant differences in the accreted refractory abundance ratios for those white dwarfs with or without circumstellar gas, but there is tentative evidence for those with circumstellar gas discs to be accreting more water rich material which may suggest that volatiles accrete earlier in a gas-rich phase., Comment: Accepted for publication in MNRAS

We analyze ionized gas emission lines in deep rest-frame optical spectra of 16 quiescent galaxies at redshift $1.7

The signal from a transiting planet can be diluted by astrophysical contamination. In the case of circumstellar debris disks, this contamination could start in the mid-infrared and vary as a function of wavelength, which would then change the observed transmission spectrum for any planet in the system. The MIRI/LRS WASP-39b transmission spectrum shows an unexplained dip starting at $\sim$10 $\mu$m that could be caused by astrophysical contamination. The spectral energy distribution displays excess flux at similar levels to that which are needed to create the dip in the transmission spectrum. In this article, we show that this dip is consistent with the presence of a bright circumstellar debris disk, at a distance of $>$2 au. We discuss how a circumstellar debris disk like that could affect the atmosphere of WASP-39b. We also show that even faint debris disks can be a source of contamination in MIRI exoplanet spectra., Comment: accepted to ApJL

This monograph offers a toolbox of mathematical techniques, which have been effective and widely applicable in information-theoretic analysis. The first tool is a generalization of the method of types to Gaussian settings, and then to general exponential families. The second tool is Laplace and saddle-point integration, which allow to refine the results of the method of types, and are capable of obtaining more precise results. The third is the type class enumeration method, a principled method to evaluate the exact random-coding exponent of coded systems, which results in the best known exponent in various problem settings. The fourth subset of tools aimed at evaluating the expectation of non-linear functions of random variables, either via integral representations, or by a refinement of Jensen's inequality via change-of-measure, by complementing Jensen's inequality with a reversed inequality, or by a class of generalized Jensen's inequalities that are applicable for functions beyond convex/concave. Various application examples of all these tools are provided along this monograph., Comment: 154 pages, 1 figure, submitted for publication

In many sequential decision problems, an agent performs a repeated task. He then suffers regret and obtains information that he may use in the following rounds. However, sometimes the agent may also obtain information and avoid suffering regret by querying external sources. We study the trade-off between the information an agent accumulates and the regret it suffers. We invoke information-theoretic methods for obtaining regret lower bounds, that also allow us to easily re-derive several known lower bounds. We introduce the first Bayesian regret lower bounds that depend on the information an agent accumulates. We also prove regret upper bounds using the amount of information the agent accumulates. These bounds show that information measured in bits, can be traded off for regret, measured in reward. Finally, we demonstrate the utility of these bounds in improving the performance of a question-answering task with large language models, allowing us to obtain valuable insights.

Ensuring robust 3D object detection and localization is crucial for many applications in robotics and autonomous driving. Recent models, however, face difficulties in maintaining high performance when applied to domains with differing sensor setups or geographic locations, often resulting in poor localization accuracy due to domain shift. To overcome this challenge, we introduce a novel diffusion-based box refinement approach. This method employs a domain-agnostic diffusion model, conditioned on the LiDAR points surrounding a coarse bounding box, to simultaneously refine the box's location, size, and orientation. We evaluate this approach under various domain adaptation settings, and our results reveal significant improvements across different datasets, object classes and detectors.

The imminent era of error-corrected quantum computing urgently demands robust methods to characterize complex quantum states, even from limited and noisy measurements. We introduce the Quantum Attention Network (QuAN), a versatile classical AI framework leveraging the power of attention mechanisms specifically tailored to address the unique challenges of learning quantum complexity. Inspired by large language models, QuAN treats measurement snapshots as tokens while respecting their permutation invariance. Combined with a novel parameter-efficient mini-set self-attention block (MSSAB), such data structure enables QuAN to access high-order moments of the bit-string distribution and preferentially attend to less noisy snapshots. We rigorously test QuAN across three distinct quantum simulation settings: driven hard-core Bose-Hubbard model, random quantum circuits, and the toric code under coherent and incoherent noise. QuAN directly learns the growth in entanglement and state complexity from experimentally obtained computational basis measurements. In particular, it learns the growth in complexity of random circuit data upon increasing depth from noisy experimental data. Taken to a regime inaccessible by existing theory, QuAN unveils the complete phase diagram for noisy toric code data as a function of both noise types. This breakthrough highlights the transformative potential of using purposefully designed AI-driven solutions to assist quantum hardware.

The reliance on wireless network architectures for applications demanding high reliability and fault tolerance is growing. These architectures heavily depend on wireless channels, making them susceptible to impairments and blockages. Ensuring functionality, particularly for safety-critical applications, demands robust countermeasures at the physical layer. In response, this work proposes the utilization of a dynamic Rate Splitting (RS) grouping approach as a resilience mechanism during blockages. RS effectively manages interference within networks but faces challenges during outages and blockages, where system performance can deteriorate due to the lowest decoding rate dictating the common rate and increased interference from fewer available channel links. As a strategic countermeasure, RS is leveraged to mitigate the impact of blockages, maintaining system efficiency and performance amidst disruptions. In fact, the introduction of new RS groups enables the exploration of novel solutions to the resource allocation problem, potentially outperforming those adopted before the occurrence of a blockage. As it turns out, by employing the dynamic RS grouping, the network exhibits an antifragile recovery response, showcasing the network's ability to not only recover from disruptions but also surpass its initial performance., Comment: 6 pages, 2 figures, submitted to 19th International Symposium on Wireless Communication Systems (ISWCS 2024)

The integration of Reconfigurable Intelligent Surfaces (RIS) in 6G wireless networks offers unprecedented control over communication environments. However, identifying optimal configurations within practical constraints remains a significant challenge. This becomes especially pronounced, when the user is mobile and the configurations need to be deployed in real time. Leveraging Ultra-Wideband (UWB) as localization technique, we capture and analyze real-time movements of a user within the RIS-enabled indoor environment. Given this information about the system's geometry, a model-based optimization is utilized, which enables real-time beam steering of the RIS towards the user. However, practical limitations of UWB modules lead to fluctuating UWB estimates, causing the RIS beam to occasionally miss the tracked user. The methodologies proposed in this work aim to increase the compatibility between these two systems. To this end, we provide two key solutions: beam splitting for obtaining more robust RIS configurations and UWB estimation correction for reducing the variations in the UWB data. Through comprehensive theoretical and experimental evaluations in both stationary and mobile scenarios, the effectiveness of the proposed techniques is demonstrated. When combined, the proposed methods improve worst-case tracking performance by a significant 17.5dB compared to the conventional approach., Comment: 6 pages, 12 figures, submitted to 19th International Symposium on Wireless Communication Systems (ISWCS 2024)

We consider a molecular channel, in which messages are encoded to the frequency of objects (or concentration of molecules) in a pool, and whose output during reading time is a noisy version of the input frequencies, as obtained by sampling with replacement from the pool. We tightly characterize the capacity of this channel using upper and lower bounds, when the number of objects in the pool of objects is constrained. We apply this result to the DNA storage channel in the short-molecule regime, and show that even though the capacity of this channel is technically zero, it can still achieve a large information density.

We investigate the fundamental limits of reliable communication over multi-view channels, in which the channel output is comprised of a large number of independent noisy views of a transmitted symbol. We consider first the setting of multi-view discrete memoryless channels and then extend our results to general multi-view channels (using multi-letter formulas). We argue that the channel capacity and dispersion of such multi-view channels converge exponentially fast in the number of views to the entropy and varentropy of the input distribution, respectively. We identify the exact rate of convergence as the smallest Chernoff information between two conditional distributions of the output, conditioned on unequal inputs. For the special case of the deletion channel, we compute upper bounds on this Chernoff information. Finally, we present a new channel model we term the Poisson approximation channel -- of possible independent interest -- whose capacity closely approximates the capacity of the multi-view binary symmetric channel for any fixed number of views., Comment: 33 pages, 1 figure, submitted to the IEEE

The Pyramid Wavefront Sensor (PyWFS) is highly nonlinear and requires the use of beam modulation to successfully close an AO loop under varying atmospheric turbulence conditions, at the expense of a loss in sensitivity. In this work we train, analyse, and compare the use of deep neural networks (NNs) as non-linear estimators for the non-modulated PyWFS, identifying the most suitable NN architecture for reliable closed-loop AO. We develop a novel training strategy for NNs that seeks to accommodate for changes in residual statistics between open and closed-loop, plus the addition of noise for robustness purposes. Through simulations, we test and compare several deep NNs, from classical to new convolutional neural networks (CNNs), plus a state-of-the-art transformer neural network (TNN, Global Context Visual Transformer, GCViT), first in open-loop and then in closed-loop. Using open-loop simulated data, we observe that a TNN (GCViT) largely surpasses any CNN in estimation accuracy in a wide range of turbulence conditions. Also, the TNN performs better in simulated closed-loop than CNNs, avoiding estimation issues at the pupil borders. When closing the loop at strong turbulence and low noise, the TNN using non-modulated PyWFS data is able to close the loop similar to a PyWFS with $12\lambda/D$ of modulation. When raising the noise only the TNN is able to close the loop, while the standard linear reconstructor fails, even with modulation. Using the GCViT, we close a real AO loop in the optical bench achieving a Strehl ratio between 0.28 and 0.77 for turbulence conditions ranging from 6cm to 20cm, respectively. In conclusion, we demonstrate that a TNN is the most suitable architecture to extend the dynamic range without sacrificing sensitivity for a non-modulated PyWFS. It opens the path for using non-modulated Pyramid WFSs under an unprecedented range of atmospheric and noise conditions., Comment: 8 pages, 9 figures

Massive quiescent galaxies in the young universe are expected to be quenched rapidly, but it is unclear whether they all experience starbursts before quenching and what physical mechanism drives rapid quenching. We study 16 massive quiescent galaxies ($\log(M_\star/M_\odot) > 10$) at $z\sim2$ selected from a representative sample of the Blue Jay survey. We reconstruct their star formation histories by fitting spectral energy distribution models to the JWST/NIRSpec $R\sim1000$ spectra. We find that massive quiescent galaxies can be split into three categories with roughly equal numbers of galaxies according to their SFHs: 1) Relatively old galaxies quenched at early epochs; 2) Galaxies that are rapidly and recently quenched after a flat or bursty formation history (depending on the assumed prior); 3) Galaxies that are rapidly and recently quenched after a major starburst. Most recently quenched galaxies show neutral gas outflows, probed by blueshifted $\rm Na\,I\,D$ absorption, and ionized gas emission, with line ratios consistent with active galactic nucleus (AGN) diagnostics. This suggests that AGN activity drives multi-phase gas outflows, leading to rapid quenching. By tracing back the SFHs of the entire sample, we predict the number density of massive quiescent galaxies at $z=4-6$: $n=3.0\pm1.4\times10^{-5}\,\rm Mpc^{-3}$. The two oldest massive quiescent galaxies in our sample appear to have extremely early formation and quenching ($z\gtrsim6$), possibly descendants of early post-starbursts at $z>3$. These galaxies still show neutral gas reservoirs and low-level star formation, consistent with weak H$\alpha$ emission, perhaps because the ejective AGN feedback that caused rapid quenching has weakened over time., Comment: Submitted to ApJ; 21 pages, 9 figures, 3 tables (excluding appendix)

We consider the one-dimensional stochastic differential equation \begin{equation*} X_t = x_0 + L_t + \int_0^t \mu(X_s)ds, \quad t \geq 0, \end{equation*} where $\mu$ is a finite measure of Kato class $K_{\eta}$ with $\eta \in (0,\alpha-1]$ and $(L_t)_{t \geq 0}$ is a symmetric $\alpha$-stable process with $\alpha \in (1,2)$. We derive weak and strong well posedness for this equation when $\eta \leq\alpha-1$ and $\eta < \alpha-1$, respectively, and show that the condition $\eta \leq \alpha-1$ is sharp for weak existence. We furthermore reformulate the equation in terms of the local time of the solution $(X_{t})_{t \geq 0}$ and prove its well posedness. To this end, we also derive a Tanaka-type formula for a symmetric, $\alpha$-stable processes with $\alpha \in (1,2)$ that is perturbed by an adapted, right-continuous process of finite variation.

A rectilinear drawing of a graph is a drawing of the graph in the plane in which the edges are drawn as straight-line segments. The rectilinear crossing number of a graph is the minimum number of pairs of edges that cross over all rectilinear drawings of the graph. Let $n \ge r$ be positive integers. The graph $K_n^r$, is the complete $r$-partite graph on $n$ vertices, in which every set of the partition has at least $\lfloor n/r \rfloor$ vertices. The layered graph, $L_n^r$, is an $r$-partite graph on $n$ vertices, in which for every $1\le i \le r-1$, all the vertices in the $i$-th partition are adjacent to all the vertices in the $(i+1)$-th partition. In this paper, we give upper bounds on the rectilinear crossing numbers of $K_n^r$ and~$L_n^r$.

This work introduces a novel Augmented Reality (AR) approach to visualize material data alongside real objects in order to facilitate detailed material analyses based on spatial non-destructive testing (NDT) data as generated in X-ray computed tomography (XCT) imaging. For this purpose, we introduce a framework that leverages the potential of AR devices, visualization and interaction techniques to seamlessly explore complex primary and secondary XCT data matched with real-world objects. The overall goal of the proposed analysis scheme is to enable researchers and analysts to inspect material properties and structures onsite and in-place. Coupling immersive visualization techniques with real physical objects allows for highly intuitive workflows in material analysis and inspection, which enables the identification of anomalies and accelerates informed decision making. As a result, this framework generates an immersive experience, which provides a more engaging and more natural analysis of material data. A case study on fiber-reinforced polymer datasets was used to validate the AR framework and its new workflow. Initial results revealed positive feedback from experts, in particular regarding improved understanding of spatial data and a more natural interaction with material samples, which may have significant potential when combined with conventional analysis systems., Comment: 16 pages, 4 figures

Accurate 3D object detection is crucial to autonomous driving. Though LiDAR-based detectors have achieved impressive performance, the high cost of LiDAR sensors precludes their widespread adoption in affordable vehicles. Camera-based detectors are cheaper alternatives but often suffer inferior performance compared to their LiDAR-based counterparts due to inherent depth ambiguities in images. In this work, we seek to improve monocular 3D detectors by leveraging unlabeled historical LiDAR data. Specifically, at inference time, we assume that the camera-based detectors have access to multiple unlabeled LiDAR scans from past traversals at locations of interest (potentially from other high-end vehicles equipped with LiDAR sensors). Under this setup, we proposed a novel, simple, and end-to-end trainable framework, termed AsyncDepth, to effectively extract relevant features from asynchronous LiDAR traversals of the same location for monocular 3D detectors. We show consistent and significant performance gain (up to 9 AP) across multiple state-of-the-art models and datasets with a negligible additional latency of 9.66 ms and a small storage cost., Comment: Accepted by ICRA 2024. The code can be found at https://github.com/YurongYou/AsyncDepth

Large language models (LLM), such as Google's Minerva and OpenAI's GPT families, are becoming increasingly capable of solving mathematical quantitative reasoning problems. However, they still make unjustified logical and computational errors in their reasoning steps and answers. In this paper, we leverage the fact that if the training corpus of LLMs contained sufficiently many examples of formal mathematics (e.g. in Isabelle, a formal theorem proving environment), they can be prompted to translate i.e. autoformalize informal mathematical statements into formal Isabelle code -- which can be verified automatically for internal consistency. This provides a mechanism to automatically reject solutions whose formalized versions are inconsistent within themselves or with the formalized problem statement. We evaluate our method on GSM8K, MATH and MultiArith datasets and demonstrate that our approach provides a consistently better heuristic than vanilla majority voting -- the previously best method to identify correct answers, by more than 12% on GSM8K. In our experiments it improves results consistently across all datasets and LLM model sizes. The code can be found at https://github.com/jinpz/dtv., Comment: ICLR 2024

Categories of lenses/optics and Dialectica categories are both comprised of bidirectional morphisms of basically the same form. In this work we show how they can be considered a special case of an overarching fibrational construction, generalizing Hofstra's construction of Dialectica fibrations and Spivak's construction of generalized lenses. This construction turns a tower of Grothendieck fibrations into another tower of fibrations by iteratively twisting each of the components, using the opposite fibration construction., Comment: v3: 18 pp. Project results from the American Mathematical Society's Math Research Community on Applied Category Theory 2022. Final version for proceedings of MFPS 2024. Updated author affiliation

The chemical composition of an extrasolar planet is fundamental to its formation, evolution and habitability. In this study, we explore a new way to measure the chemical composition of the building blocks of extrasolar planets, by measuring the gas composition of the disrupted planetesimals around white dwarf stars. As a first attempt, we used the photo-ionization code Cloudy to model the circumstellar gas emission around a white dwarf Gaia J0611$-$6931 under some simplified assumptions. We found most of the emission lines are saturated and the line ratios approaching the ratios of thermal emission; therefore only lower limits to the number density can be derived. Silicon is the best constrained element in the circumstellar gas and we derived a lower limit of 10$^{10.3}$ cm$^{-3}$. In addition, we placed a lower limit on the total amount of gas to be 1.8 $\times$ 10$^{19}$ g. Further study is needed to better constrain the parameters of the gas disk and connect it to other white dwarfs with circumstellar gas absorption., Comment: 14 pages, 10 figures, 4 table, accepted for publication in AJ

Standard information theory says nothing about how much meaning is conveyed by a message. We fill this gap with a rigorously justifiable, quantitative definition of ``pragmatic information'', the amount of meaning in a message relevant to a particular decision. We posit that such a message updates a random variable, $\omega$, that informs the decision. The pragmatic information of a single message is then defined as the Kulbach-Leibler divergence between the apriori and aposteriori probabilities of $\omega$; the pragmatic information of a message ensemble is the expected value of the pragmatic information of the ensemble's component messages. We justify these definitions by proving that the pragmatic information of a single message is the expected difference between the shortest binary encoding of $\omega$ under the a priori and a posteriori distributions, and that the average of the pragmatic values of individual messages, when sampled a large number of times from the ensemble, approaches its expected value. Pragmatic information is non-negative and additive for independent decisions and ``pragmatically independent'' messages. Also, pragmatic information is the information analogue of free energy: just as free energy quantifies the part of a system's total energy available to do useful work, so pragmatic information quantifies the information actually used in making a decision. We sketch 3 applications: the single play of a slot machine, a.k.a. a ``one armed bandit'', with an unknown payout probability; a characterization of the rate of biological evolution in the so-called ``quasi-species'' model; and a reformulation of the efficient market hypothesis of finance. We note the importance of the computational capacity of the receiver in each case., Comment: 15 pages, no figures

We provide a generalized treatment of (co)cartesian arrows, fibrations, and functors. Compared to the classical conditions, the endpoint inclusions get replaced by arbitrary shape inclusions. Our framework is Riehl--Shulman's simplicial homotopy type theory which supports the development of synthetic internal $(\infty,1)$-category theory., Comment: 19 pages. This text is based on Appendix A from author's PhD thesis arXiv:2202.13132. Comments welcome!

We propose a game-based formulation for learning dimensionality-reducing representations of feature vectors, when only a prior knowledge on future prediction tasks is available. In this game, the first player chooses a representation, and then the second player adversarially chooses a prediction task from a given class, representing the prior knowledge. The first player aims is to minimize, and the second player to maximize, the regret: The minimal prediction loss using the representation, compared to the same loss using the original features. For the canonical setting in which the representation, the response to predict and the predictors are all linear functions, and under the mean squared error loss function, we derive the theoretically optimal representation in pure strategies, which shows the effectiveness of the prior knowledge, and the optimal regret in mixed strategies, which shows the usefulness of randomizing the representation. For general representations and loss functions, we propose an efficient algorithm to optimize a randomized representation. The algorithm only requires the gradients of the loss function, and is based on incrementally adding a representation rule to a mixture of such rules., Comment: ICLR 2024

The heavy fermion material UTe$_2$ possesses a rich phase diagram with multiple superconducting phases, several of which exhibit characteristics of odd-parity pairing. Here, we report on the pressure dependence of signatures of the superconducting transition in the temperature dependent ac magnetic susceptibility $\chi(T)$ in high quality UTe$_2$ single crystals. We resolve a single superconducting transition in $\chi(T)$ at low pressures $<$ 0.3 GPa. At higher pressure, however, a second feature emerges in $\chi(T)$, which is located at the thermodynamic phase boundary between two separate superconducting states previously identified by specific heat studies. The observation of a two-step transition in $\chi(T)$ can be understood as a consequence of the change in the London penetration depth, when UTe$_2$ switches from one superconducting phase into another.

The phase landscape of UTe$_2$ features a remarkable diversity of superconducting phases under applied pressure and magnetic field. Recent quantum oscillation studies at ambient pressure have revealed the quasi-2D Fermi surface of this material. However, the pressure-dependence of the Fermi surface remains an open question. Here we track the evolution of the UTe$_2$ Fermi surface as a function of pressure up to 19.5 kbar by measuring quantum interference oscillations. We find that in sufficient magnetic field to suppress both superconductivity at low pressures and incommensurate antiferromagnetism at higher pressures, the quasi-2D Fermi surface found at ambient pressure smoothly connects to that at 19.5 kbar, with no signs of a reconstruction over this pressure interval. The warping of the cylindrical Fermi sheets continuously increases with pressure, which is consistent with increased $f$-orbital contribution at the Fermi level, up to and beyond the critical pressure at which superconductivity is truncated. These findings highlight the value of high pressure quantum interference measurements as a new probe of the electronic structure in heavy fermion materials.

Quantum critical phenomena are widely studied across various materials families, from high temperature superconductors to magnetic insulators. They occur when a thermodynamic phase transition is suppressed to zero temperature as a function of some tuning parameter such as pressure or magnetic field. This generally yields a point of instability - a so-called quantum critical point - at which the phase transition is driven exclusively by quantum mechanical fluctuations. Here we show that the heavy fermion metamagnet UTe$_2$ possesses a quantum phase transition at extreme magnetic field strengths of over 70 T. Surprisingly, rather than terminating at one singular point, we find that the phase boundary is sensitive to magnetic field components in each of the three cartesian axes of magnetic field space. This results in the three-dimensional transition surface being bounded by a continuous ring of quantum critical points, the locus of which forms an extended line of quantum criticality - a novel form of quantum critical phase boundary. Within this quantum critical line sits an intensely field-resilient superconducting state in a striking toroidal shape, persisting to fields over 70 T. We model our data by a phenomenological free energy expansion, and show how a three-dimensional quantum critical phase boundary - rather than a more conventional singular point of instability - anchors the remarkable high magnetic field phase landscape of UTe$_2$.